From d86a673e1be70962504c8e44af71723c2a0d1a79 Mon Sep 17 00:00:00 2001 From: Cyril Cohen Date: Wed, 19 Dec 2018 15:43:31 +0100 Subject: Generalizing homo-mono-morphism lemmas and extremum (#201) --- mathcomp/ssreflect/seq.v | 6 ++++++ 1 file changed, 6 insertions(+) (limited to 'mathcomp/ssreflect/seq.v') diff --git a/mathcomp/ssreflect/seq.v b/mathcomp/ssreflect/seq.v index a574710..a9cc2ac 100644 --- a/mathcomp/ssreflect/seq.v +++ b/mathcomp/ssreflect/seq.v @@ -1842,6 +1842,12 @@ Proof. by rewrite -[s1 in subseq s1]cats0 cat_subseq ?sub0seq. Qed. Lemma suffix_subseq s1 s2 : subseq s2 (s1 ++ s2). Proof. exact: cat_subseq (sub0seq s1) _. Qed. +Lemma take_subseq s i : subseq (take i s) s. +Proof. by rewrite -[s in X in subseq _ X](cat_take_drop i) prefix_subseq. Qed. + +Lemma drop_subseq s i : subseq (drop i s) s. +Proof. by rewrite -[s in X in subseq _ X](cat_take_drop i) suffix_subseq. Qed. + Lemma mem_subseq s1 s2 : subseq s1 s2 -> {subset s1 <= s2}. Proof. by case/subseqP=> m _ -> x; apply: mem_mask. Qed. -- cgit v1.2.3